Let R and S be rings and RωS a semidualizing bimodule. We investigate when the double
functor TorS i (ω, Exti R (ω,−)) preserves epimorphisms and the double functor Exti R (ω …

1. Introduction Throughout this paper, all rings are associative rings with units. For a ring R, we
use Mod R to denote the cate Page 1 EXTENSION CLOSURE OF ADJOINT COTORSIONFREE …

Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …

Given a ring $ R $, two classes $\mathcal A $ and $\mathcal B $ of $ R $-modules are said
to form a cotorsion pair $(\mathcal A,\mathcal B) $ in $\operatorname {Mod} R $ if $\mathcal …

Let R be a left Noetherian ring, S a right Noetherian ring and RU a generalized tilting
module with S= End (RU). We give some equivalent conditions that the injective dimension …

Let R be a commutative Noetherian ring with identity and C a semidualizing module for R.
Let 𝒫 C (R) and ℐ C (R) denote, respectively, the classes of C-projective and C-injective R …

Several authors have been interested in cotorsion theories. Among these theories we figure
the pairs $(\mathcal P_n,\mathcal P_n^{\perp}) $, where $\mathcal P_n $ designates the set …

Let R be a Noetherian ring and I an ideal of R. Let M be an I-cofinite and N a finitely
generated R-module. It is shown that the R-modules $ Tor_ {i}^{R}(N, M) $ are I-cofinite for …

Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1
R (G, M)= 0 for any flat R-module G. It is well known that each pure-injective left R-module is …

Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …